How many whole numbers lie in the interval between $\frac{5}{3}$ and $2\pi$ ?
The smallest whole number in the interval is 2 because $\frac{5}{3}$ is more than 1 but less than 2. The largest whole number in the interval is 6 because $2\pi$ is more than 6 but less than 7. There are $\boxed{5}$ whole numbers in the interval. They are 2, 3, 4, 5, and 6.